Stability theory, Permutations of Indiscernibles, and Embedded Finite Models∗

Abstract

We show that the expressive power of first-order logic over finite models embedded in a model M is determined by stability-theoretic properties of M . In particular, we show that if M is stable, then every class of finite structures that can be defined by embedding the structures in M , can be defined in pure first-order logic. We also show that if M does… (More)

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